Digital-to-analog conversion, which may include oversampling or shaping the quantization noise of a digital signal, is well-known and has a wide variety of applications, including digital audio, digital telephony, and digital instrumentation, to name only a few. Digital-to-analog conversion is discussed, for example, in "Oversampling Methods for A/D and D/A Conversion," by James C. Candy and Gabor C. Temes, appearing in the text Oversampling Delta-Sigma Data Converters: Theory, Design and Simulation, edited by James C. Candy and Gabor C. Temes, and published by IEEE Press (1992), "Oversampled, Linear Predictive and Noise-Shaping Coders of Order N&gt;1," by Stuart K. Tewksbury and Robert W. Hallock, and appearing in the aforementioned Candy and Temes text, "Optimal Nonrecursive Noise Shaping Filters for Oversampling Data Converters, Part 1: Theory" and "Optimal Nonrecursive Noise Shaping Filters for Oversampling Data Converters, Part 2: Applications" by Steven R. Norsworthy, appearing in IEEE Proc. ISCAS '93, Vol. 2, pp 1353-1360, May 1993, all of the foregoing herein incorporated by reference. One conversion technique, described in "A 16 -bit Fourth Order Noise-Shaping D/A Converter," by L. R. Candy and John Kenney, also appearing in the Candy and Temes text, includes coupling a sigma-delta modulator to a conventional digital-to-analog converter, which is then followed by a lowpass analog filter. It will be appreciated that the terms delta-sigma modulator and sigma-delta modulator are generally used interchangeably in this context. The digital-to-analog conversion technique of the Carley and Kenney paper relaxes the constraints on the lowpass analog filter and reduces the amount of out-of-band noise present in the signal provided to the lowpass analog filter where a multibit sigma-delta modulator is used. However, the problems associated with achieving precise quantization level conversion in the conventional digital-to-analog converter coupled to the multibit sigma-delta modulator are well-known. Furthermore, all N-bits of an N-bit digital signal must be processed in the architecture of the Carley and Kenney paper. This large data path, thus, introduces some significant hardware complexity for the sigma-delta modulator.
Another approach or technique is employed in the Burr-Brown PCM67 Digital-to-Analog (D/A) Converter chip described on pages 6.2.189-6.2.192 of the Burr-Brown IC Databook Supplement, Vol. 33c, herein incorporated by reference. This chip uses a 10-bit conventional digital-to-analog converter (DAC) for the upper or most significant 10 bits of an 18-bit digital input signal. It also uses a 1-bit first-order sigma-delta modulator for the lower or least significant 8 bits of the 18-bit digital input signal. The sigma-delta modulator employs oversampling at 384 times the Nyquist rate, producing a 1-bit digital signal that is provided to a 1-bit DAC. The analog output currents from the 10-bit DAC and the 1-bit DAC are then summed to provide the analog output signal for the chip.
The "Burr-Brown" approach, although reducing the problems associated with quantization level conversion of the output signal of a conventional multibit sigma-delta modulator, has other disadvantages. In particular, the accuracy of the analog output signal produced is limited by the accuracy of combining the analog output currents from the two DACs. In addition, any direct current (DC) offset, slew rate limiting, thermal noise and other analog device anomalies will result in imperfect cancellation of the truncation error that occurs when the 18-bit digital input signal is truncated to provide the 10-bit digital signal for the 10-bit DAC. Furthermore, the truncation error fed to the 1-bit first-order sigma-delta modulator may overload its 1-bit quantizer, resulting in nonlinearities that may not be easily removed. This problem may be even worse for a sigma-delta modulator having an order higher than first order. This situation may, therefore, ultimately degrade the noise floor of the digital output signal produced by the 1-bit sigma-delta modulator. Furthermore, as is well-known, a 1-bit first-order sigma-delta modulator introduces significant pattern noise in its output signal. Thus, a need exists for a device or method for digitally shaping the quantization noise of a N-bit digital signal, such as for use in digital-to-analog conversion, that reduces or diminishes the foregoing problems.